{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UBdEJA2KPI/3KkDhpSZrvq2cI3582kO9PG8jpwnLe3nOGt/bkcqqwnL+sz+RvG08wc2Qsv5s/mojgzvk6O3JEDZbriM7aQX/9rmC4MekOdHf0WD/bSVe6U7+Ukr/uLOGLnEp+P6MnA6LUhfb+8ZFEBvrg7+taFxG4v/779gjmRzMG88D0QWzLKuT/tuWw7uB5jl0oJSyw81ry8rpBpJvQWTvor98VPGHRoolJhxFCEB7gg4+AzMLGu4aYEN8uMSRtsXXrVl588cWG7++++y5CCI4cOdKQVlFRwbRp06itrWXdunUMHDiQO++8k/79+3O4fi6qA77zne9wy6ThbPrdXXy57DqeXZKC1VrDNddcw+mCy8z/+5d8duhCdx2eiYlLeKUxCQkxWoFrJCeXtZ/Jg+lK/WcuW3l6axGbchq9dy4YFsrfb+zFDQO7J6SdI/19+/YlNTW14fvKlSuZMmVKE+eP//nPf1iwYAG+vr4kJSVx9913s3z5chYtWsTw4cPbLPeee+5h3bp1AMRFBDI6IRJ/f3+mT5/OQ8v/wdenink3o/2JjOPbnJ7i2bhDe0fCCNjfFDiiurqaa665BqvdIK3Ode8qXmlMPGCCmktYrd17h93ddIX+kspa/rm7hB9/nM+2M1W8fbiU+pmHYQE+7c7IcgVH+u2NSWlpKVu2bOGFF17g9ddfb8jz6quvcssttwCwd+9eUlJS2LNnDykpKe2We80119CjR48W6fPmzaPkwAYenzuCH88Y3JB++Nwljp6/3Ir+dovyWNyhfevWre3msb8pcES9oX/jjTca0nSue1fxSmNi+uYyFlf019RJPjhWxn3r8vkkSz2NzOgfxOPTejg9oN5ZHOmvq6truFN97733mDVrFkOGDKFnz57s3r2b6upqsrKySEpKAmDfvn2kpqZSWFhIUf0ydydITk5m965dfHtKfwbFKE8BUkoefWc/s//8BY+/d4CS8sYuv3DjPbo4TXg4HDhwoMnTw549e5g+fXqn91VWVsaNN95ISkoKycnJDRf90FDl2SE7O5vhw4fzve99j5EjR3LDDTdQYXNNYH9TAHDttdfy6aefAvDYY49x//33A8rQv/rqq030X6noPdLrgMstb9a0YteuMJKS9PJvZY+z+g9erOZfu0vIvawu2FfF+XNPSjgJ4e5tpo70b9u2jYMHD3LPPfewcuVKfvSjHwFw6623snLlSuLj44m08/T329/+FlDdV67g6+uLv78/ly9fJixMGZMqax3JfSLYm1vCy1/l8OG+c/x85lCWpPVl40bBsGEuFWkYGzfC0qUjyMrKora2Fl9fXx588EGeffbZJvmmTp3K5VZO9GeeeYYZM2YAsG7dOnr37s2aNWsAKClpGY75+PHjrFy5kueff54lS5bw1ltvsWTJkiY3BQC/+tWvePzxx8nLy+Prr7/m/fffB5Sh37lzZxP9uta9q3ilMTHRi0tVdby87zIbstVdYXyoL99KDWNsvGcF2UpMTKR///4UFhayfv169u/fjxCC2tpahBA8+uijVNrNS2/rSaqzi4WrqqoIDGysj0CLL0/eksztExL55XsH2X6ykIff3s/be86QUj0KCO308XkKPj4+jBw5koMHD3L8+HH69evHmDFNI09s3ry53f2MGjWKn/70pyxbtoy5c+cytd5plh39+/dv6LocO3Ys2dnZ5OfnN7kpANUFKaXk2WefZePGjQ3dX60Z+isVs5vLAwkOrms/kwfTGf1bT1fyo3UX2ZBdgZ8PfGNEKH+6IdpQQ+JIf0JCAqNHj2b16tV885vfJCcnh+zsbE6fPk3//v3Zv38/tbW1DQZFSunwNX36dM6c6ZhXoIKCAqKjo7FYWq43GRYXzutLJ/LnW1OJDg1gR3Yh/zm3mec+P05NrX7tyNYDxcSJE/nyyy954okneOqpp1rkmzp1KqmpqS1en332WUOeIUOGsGfPHkaNGsVjjz3Gk08+2WI/AXYuxn19fbFarQQFBTW5KQDYv38/586dw9/fv4XRsDf0ofracJfxSmOi+x+amlpqtASX6Kj+v+8q4Y/birlULRnZy58/3RDNkpGhWLp5im97ONJfW1tLTU0NK1euZP78+U22LVy4kJUrV3LDDTewxea69t133+V73/se3/jGN/jkk08a8tbV1ZGZmdlisP22225j0qRJHD16lISEBF544QUANmzYwI033uhQrxCCW1L78PmD0/hGWl9qZR1//PQY8//+Jccu6NXnO2WKep84cSKPPfYY8+fPp0+fPi3ybd68mYyMjBav+i4ugLNnzxIcHMydd97Jz372M/bUu2Vuh6ioqCY3BefOneOOO+7gvffeIzQ0tGHGHbQ09PX6r0S8spvLVVfKRhMYqN8dpT0d1T+0p4UvT1XyzZQwbhgQ1CmXJ92JI/3bt2/n0KFDbNiwocW2Bx54AFCDxX/605+YMWMG8+bNY968eRQVFfHQQw9xww03AHDo0CEWLlxIUFBT55KO4su/9tprLF++vF3dEcEWfr9oNNOSevPU5/s4cOYSc/+yhZ/eMITvTR2Aj4s+v9xBsG2297BhwwgICGDZsmVO72v//v387Gc/w8fHB4vFwj/+0W5cvQbqbwomT57MggUL+OMf/8jw4cP53//9X5YtW8asWSqeX3NDH9w9s9W1wCMcPXY1urugf/TRHBYs8AwX7s7w9tvRreqvskoyi2oY2csfUN1ARZV19OjGab7O4Ej/2bNn6d+/P8nJLfyRNuE///kPd999d0O/+k9/+lPuuOOOFv3+HaG6uprXX3+du+66q8O/+de/4Pa7rfx2zSFW7lChgH4xZxhLrxnY6fLdzb/+BUuXwn333ce4ceO4++67DdFRf1PwyiuvtJlvwYIFLF++nCFDhgCN+nXFFUePmt/Deyd1ej+YtKq/rKaOn39ewG82F5J7SU3GF0J4nCEBx/Xfu3fvdg0JwLe//W18fX2RUrJs2TJmz57tlCEBtZahM4YElP7QAD9+t2A0/71nHOOTenDHhH5Ole9uLlw4wbBhw6ioqDDMkACMGTOGa6+9tt1Fi/PmzWswJKD/uesKXtnNZeJ5hFh8GBTlh5SSOk2fhmtqaqisrGwyq6otnnvuOT777DNKSkrIzMzkXgOiJl07LIb0ob0aZpZVVNfy8lfZfHtKfyzdFJzLFXr1GtjEPY2RfPvb325zuzOG3pvxym6u0aPT5L59+nZzrVmzj7g4fb1Vnj9vIS6uhqpayeWqOqKD1dNHpVXdtgX6ed5FzJ56/c3ZunUrYWFhLq8b6W5OnVKhWltj2ep9vLHrNAvHJPDHJe2vync3bWnXAd31m91czdDda3B93HJdyc+3kFdm5bH1Bfx6cxEVNY1GxNMNCTiu//79+zNhwgQ3q+k89THEW2NxWgL9o0NYes0A9wnqBG1pb05xsYo970l0Rr+34ZXdXLo/bOnum+v4pQqe/qyA0mpJbIgvRZV1BFk834jU46j+4+Pj23XW6Am0dTOVltSDzx6c1iSa47asAib0d5+7mrboyI1gXR1s3QqHDoEQMH8+REd3v7aOoPuNrCvoc4Z3goqK9vN4MpmZQe1n8kCklHyUWcarZ85RWi0ZExfAH2b0pHeYXvcsjuq/urqa8vJyN6vpPPv3t73d3pCs2nmaW/+1jWVv7aPaavzocXvaq6pg7VplSEDdOJZ60LKs9vR7M15pTEzcj7VO8q89l/j315eRwIJhITwyJZJQf+9pYrt27WLVqlVGy+hSgvx9CbT4sGpXLne+sJ3CsmqjJTmkuBjeeQfOnm1MGzgQ+ukxUc3r8Z4z3Q5/f6MVuEZ8vOee0K1RVlPHbzcX8UlWBRYfmB0Zxx2jwjxmEWJncVT/AwcOZNKkSW5W03k6c3G9KaU3b35/MrHhAew4Wci8v31JZp5xq+Ydac/NhXffhUuXGtPS0mD6dNXV5SlcyYbNK41JKy6MtKJHD32CIuSV1fLo+kL25VUTEeDDk+k9uDpB72XAjuo/NjaWoUOHullN54mJ6Vz+UQkRvPfDKYzqE8GpwnIW/H0r27MKukdcO7Sm/cAB+OgjqLbZeD8/uP56cHLpTrfS2br3Jgw3JkKIWUKIo0KITCHEw61sTxRCbBBCfC2E2CeEmNPePvV/MtHD/XxWUQ2PrC/g9CUrCWG+LJ/egyE9/bXR7whH+isrKyn1pA56B9h5Tu8wcRGBrPr+JK4fEculSivffGEH7+892/4Puxh77XV18MUXarC9flJNSAjcfDP07+92aR3Cmbr3Fgw1JkIIX+BvwGxgBHCbEGJEs2yPAauklFcBtwJ/b2+/LsQh8gg++yzKaAntciCvisc3FlJcWUdyL3+euq4nMSFqoF0H/W3hSP+ePXtYvXq1m9V0njffdO53Qf6+rLhzLHdN6kd1bR0PrPyaf2/O6lpx7VCvvbIS1qwB+/WLMTGeNXOrNZyte2/A6Gk244FMKWUWgBDideAW4JBdHgnUxy+LANx/u2TSglB/HwQwpW8g942PwKKBE0FXGTRoEIMHD24/o8b4+gh+dfNIEqKCeGrtEX6z5jD5pdUsmzXUbVOHi4rg44+bjo8MGgTTpukfXsKbMdqY9AFO233PBZqvCnsC+EQIcT8QAszAxHCSIi38fkZP4kJ9tR1o7ywxMTEMGjTIaBndjhCCpdcMJDo0gJ+t3seKTScoLKviqfmj8OtmFyyFhWqg3X69xvjxYItfZeLBGG1MOsJtwItSyj8KISYBrwghkqWUTSbFCyGWAksBYmISWbFCpcfFqbua+Pimj6CLFkF2NuTnq3eA5GQ13hIXp+ayg3JnP28elJWpvtv6SKHTpqnPFgts367SevWCESPU47h9WQsXwsmTarXuiRMqbfhwCAqCPn3ggw8a8y5eDMOHl7FuXRSlpeo2LDW1lMpKHwICJHv3hgAQEVHLkCHlRERYm3TLpKcXc/68PxUVvuTkqMA//fpVERRUS3x8NRs2RDbknTGjiJISP44dC6akRJU1enQZ1dWCoKA6vv5aBYYJDa0lObmMzfnFnD4exgChyps6tYRDORaqq33IylL+qhISqkhIqKK42LeJrhkziigstJCdHUhhoZ+tvsuwWgWhobXs2qUCDgUH15GaWkpgYB0bN0Y2OM6bMqWE/HwLVqtoWAcSH19Njx5W4uOrWpSVn28hNzegYTX7sGFqfUh4eC07dqiyAgPrSEu7jJ+f5MsvI6ipUUZxxIgyDhwIpq5OcOyYKis2toaoqGJ69ixh3bqIJv/X6dNqtlFurkpLSVF30NHRUB/GxN8fZs8GqxXWr29cCzV9emO3bH24jfh4GDAAevdu2o4WL1ZtNS8PcnJU2qhRqg3at9nycpWnvBy2bGlch5Geru72/fxgxw6VFhOjwszGxrY8PxKsCfwg2cKK/Xs4fAS2bBEEByldH37YVFdJCWzb1vg0MXWqOmcCAuCrr1Rajx7KKPTs2bSs+fPV8ezdq+ogIEDpCQ6GW25R+922rbGsggLIyFCGB2DyZNUtFhysjhcgIgLGjYOoqKZl3XQTnDmj6v/wYZU2cKDK378/vPVW0+PKy1NrWi5eVGkTJihDFxYGmzaptLAwpSEkRNV5/bVnzhy1Ir66Wk0iADWmEh2t3u17TBcvhnPnIDOzcRV9WpoaN4qMVG0G1DGmp6v2tGZNo9GdOVNptFph3z6V1rev+q8SE1u2o9xc5fqlPj5baqrroTsM9c1lMw5PSCln2r4/AiCl/J1dnoPALCnladv3LGCilDLP0X5HjkyTBw/q65vrjTcOMmhQZfsZ3ciR/Goe3VCIn4DnZvciJsRxf0NmZqDH6e8MjvTr4ptr/35lZLqKYxcuM7BXaJPFjl1Jba0yAkePqotbnz4qwN3Mmcrw6ERX17270dk3105gsBCivxDCHzXA/n6zPKeA6QBCiOFAIHCxrZ1W6T2ZiNzcgPYzuZlh0f7cOjKU+8ZHtGlIwDP1dwZH+gcPHsw111zjZjWdJ6uLx8yHxIY1GJKSihoef+8AZVVdM329fqD96FH1/eJF9VQyf75+hgS6vu51wtBuLimlVQhxH/Ax4Av8R0p5UAjxJLBLSvk+8FPgeSHET1CD8ffIdh6ndPeP4ymOHuuk5FJVHZGByngsHtGxeMieot9ZHOnv1asXAwZ4poNEe86d6759P/zWPj46cJ5LFTX8v1uvcmlfhYWwbl1TdyiBgTB3rr4D7d1Z956O4WMmUsq1wNpmaY/bfT4EXO1uXVc6dVLyz92X2HuhiifTe7b7NHIlUFZWRlFREVFRek99doVls4ZRUFbNQzM7v3jz7Fk1vpiYqMYN1q9veuM3caIaI9DVkFzpGG5MugPd4zDXDxYbRZ1UfrY+O1mBvw9cKLN2ypgYrd9VHOnfu3cvWVlZHj9m0p0rw5OiQ3hj6cQm04SrrXX4txNaoLYWPvtMdWvt2aMGhuuNhsWiJiIkJqrtOuOJq/LdhdFjJiYehpSSf399iU+zlCF5ZEoUo2L0HgPpKoYOHUp6errRMgzH3pD8+bPj3Pb8NkrbGUPJzFQznY4eVV1B9TOHwsLUjC2dA0qZKLzSmPhp/rwVHu447nR3IqXkhYzLfHxCOWx8eEoUo2M7b0iM0t9VONLfs2dPkjTwl+GuXriSihpW7TrN7pwivv3fnZRXOzYou3erKasXLqjz8+BB1e01fbqaMlyP7j2Iuut3Ba80JvYrZ3Wkfh2EO5FS8sr+Uj7KLMfPB5ZdHUWKE4YEjNHflTjSX1paSn5+vpvVdJ7PP3dPORFBFl773gTiwgPZkV3Id17cRWVNS0N8/LgaH6k/L0tLG9dzNQ/37i7t3YXu+l3BK42JSed583AZ7x0tw1fAzyZFclWc2bXVnH379vGh/Wo9E/r1DOG1702gV1gAX2UV8D+v7mkRZGvz5saxECHUIsEhQ9QTSkKCAaJNugWvNCauruQ0msBA90a8e/9oGW8cLMUH+PGESNJ6B7q0P3fr72oc6R82bBjTp093s5rOE+TmQJ0DeoXy6ncnEBVsYf2RPH6yKoPausbZ+8nJ6py0WGDSJNW1lZ4Ot96qVvobqb2r0V2/Kxi6Ar67GD06Te7bp+8K+DVr9hEX557FMp+dLOcfu1T/w33jIrg2yfWz4fx5i9v0dwdt6R87dqyb1XSe06eVKw13sz+3pGEwfklaAr9fOLphsL60VBmU9mZaGqW9q9Bdv84r4LsF3f0O+vm5x8Bvy63knzZD8p2rwrrEkID79HcXjvRfunSJvDyHXnw8BqMmoIxKiOA/94xrCAO8/KPGAZHQ0I5N2dd98ozu+l3BK41JSYnRClzjyy8j2s/UBfQK8SXUX/CNEaHMGRTSZft1l/7uwpH+AwcOsHbt2la3eRIffWRc2eP79+Afd47Fz0fwzy+y+OemE536vZHauwLd9buCVxoT3Xvu6r3XdjcDoyw8OzOaxSO6zpCA+/R3F470jxgxguuvv97NajpPdesh7N3GtUNjeGZxCgC/++gIq3adbucXjRit3VV01+8KXmlMTBxzvtTKl6crGr5HBfq6LeiR7kRGRtKnTx+jZWjBvKv68MubVNDUXdmFBqsxcQde2cMXHt5+Hk9m4sTuWShTUVPHr78o4nxZLT5CMCnBtVlbjugu/e7Ckf6SkhLOnz9PXFycmxV1jhtuMFqB4ltX92dgr1CmDu54nF1P0e4suut3Ba98MrF2jXdswygu7h4bH2TxYebAYAZG+ZEa698tZUD36XcXjvQfPHiQdevWuVlN5/GkdZXXDOnV8OR7ubKG04Vt+23zJO3OoLt+V9D7rPdS6uq6r9vp5qEhzB4c3K0x27tTvztwpH/kyJGMGDHCzWo6T60HerO5eLmKu/6zg/JqK2//YDI9Q1tfFOuJ2juD7vpdwSufTMr1dlrbECq2K5BS8tbhUs6XNj6udachga7VbwSO9EdERHh8Fxeo8LeeRrC/Lz4CfIWgvNrxFdcTtXcG3fW7gvlk4uV8cKyc1w6U8vGJcv46uxf+vno/NRhJcXExZ86cMQfhnSAkwI//3jMOi68PUSHd18VqYhxe+WTir3lbjY3tmtXj289U8vK+ywDcnRLmNkPSVfqNwpH+Q4cO8emnn7pZTefxVH9XMeGBDYZESsnOVmZ5ear2jqK7flfwSmNi0TtqLDExrk9WP1FUw5+3lyCB25NDubqv+7qeukK/kTjSn5yczJw5c9yspvPocEH71QeHWLziK1btbLoGRQftbaG7flfwSmOi/5OJaxfjgvJafreliKpaSXq/QBYM69pFie3hqn6jcaQ/PDycmJgYN6vpPDr4hhoap9z8/+Kd/Xx1oqAhXQftbaG7flfwSmNSVGS0Atf47DPnI+xUWuv43ZdFFFXWMbKXhXvTIty+KNEV/Z6AI/2FhYWcPt3x1dxG8eabRiton9vGJ/LdKf2x1kl+8OpuTuaXAXpobwvd9buCVxqTK5U6KXluRwkni63Ehfjys0lR3T5z60riyJEjfH4lRz/qYh6ZM5wZw2MoLq/hOy/tpKRC77G2Kx3DjYkQYpYQ4qgQIlMI8bCDPEuEEIeEEAeFEK+5W6MuvHGwlG1nqgj2EzwyJYqwAMP/Xq9i9OjRzJ0712gZXoOvj+D/3XoVw+LCyLpYxv0rv6ZO6h0L50rG0KuNEMIX+BswGxgB3CaEGNEsz2DgEeBqKeVI4Mft7Vf3OMwzZnS+n+7L0xWsPlyGD/DgpEgSwo2b9e2Mfk/Ckf7Q0FCiozvuGsQoFi82WkHHCQ3w4/m70ugR4s8Xxy5yJvpI+z/yYHSq+67G6FvX8UCmlDJLSlkNvA7c0izP94C/SSmLAKSU7QaU0N1z54ULnZtBcLK4hr/uVH73704JMzzkbmf1exqO9BcUFJCdne1eMU6gwbBOE/r2COYfd4zBz0fw6u6TnfIy7GnoVvddidGLFvsA9tWfC0xolmcIgBDiS8AXeEJK2cJBkhBiKbAUICoqkRUrVHpcHAwaBPHxTQfHFi2C7GzlS6f++pCcrGaCxcVBfdgKHx+YNw/KymDrVrislm0wbZr6bLHA9u0qrVcvGDECYmKalrVwIZw8qeKsnLCFdxg+XIX47NMHPvigMe/ixXDwYAgnTwZSWuoLQGpqKZWVPgQESPbuVTOzIiJqGTKknIgIK59/GoqFS/QhhAlRIRw4EEBFhS85Ocqo9OtXRVBQLfHx1WzYENlQ1owZRZSU+HHsWDAlJaqs0aPLqK4WBAXV8fXXoQCEhtaSnFxGaGhtk8HpqVNLuHjRQnW1D1lZymlkQkIVmZlBxMZWN8k7Y0YRhYUWsrMDKSz0s9V3GVarIDS0ll271Oye4OA6UlNLCQysY+PGSOpsvR5TppSQn2/BahVkZqppzvHx1fToYSU+vqpFWfn5FnJzA8jPV/PEhw1TbhHCw2vZsUOVFRhYR1raZfz8JF9+GdHget7XV1JTI6irEw2r4WNja6iu3k5Ozllqa+9p8n+dPg25ueoFkJICvr4QHQ2ffKLS/P1h9mzlN279eqiwOW6ePr1xwsiePdiOS4Wz7d27aTtavFi11bw8yMlRaaNGqTZo32YPHIDHH1eeILZsUVEOQYXKvXRJBXDasUOlxcTAsGEQG9vy/MjKguJi9Q6qbQcGKl0ffthUV0kJbNum9q/ahjpnAgLgq69UWo8ekJoKPXs2LWv+fBD5PbljWDIvHdrPI6sPUHIqlJSEKBIT4d13m5ZVUAAZGVBoW6YyebKKMR8crI4XICICxo1TvRT2Zd10E5w5o+r/8GGVNnCgyt+/P7z1VtOy8vLg0CG4eFGlTZgANTUQFgabNqm0sDClISQE/v1vdR0BmDMHzp9XN7cHDqi0pCTVLpKSYPXqpmWdOweZmeo3AGlpUFcHkZGqzYA6xvR01Z7WrFFaAGbOVBqtVti3T6X17av+q8TElu0oNxdOnVJ1Aep/cTXcuaFhe4UQi4BZUsrv2r5/E5ggpbzPLs+HQA2wBEgAvgBGSSmLHe23X780mZOjb9jeRx7JYdGiznmMu1xVR4Cf8IgV7qtXR3davyfhSH9ZWRmjRo0iysP7UVesgHvvNVqFcyz47QH2XM4hNjyAD+6bQkx493i27i50rnvQO2zvGcB+ZnaCLc2eXOB9KWWNlPIkcAwY7CZ9Hs3xwsb+vLAAH48wJN5MSEiIxxsS3ZneYwTjk3pw4VIVH+w7Z7Qck05gtDHZCQwWQvQXQvgDtwLvN8vzLpAOIISIRnV7ZbW1047EmvZkhgypaDfPxuwKHv68kBf3el7skI7o92Qc6b948SJZWW02PY8gJcVoBc4zJtWHv985hj8uTuE7U/obLafT6Fz3rmKoMZFSWoH7gI+Bw8AqKeVBIcSTQoibbdk+BgqEEIeADcDPpJQFre/RO/Dxab/rsVZK/HygT5jRw14t6Yh+T8aR/uPHj/PFF1+4WU3n8fU1WoHz+PpCdGgAC8c2+iWpq9OnPelc965i+JVISrkWWNss7XG7zxJ40PbqEH6GH5VrREa2H91rev9gRvbyJy7U8w62I/o9GUf6r7rqKkaNGuVmNZ1Hg9nLDmmu/ej5y/zo9a/5/cLRpPSNNERTZ9C57l3F6G6ubuGS5/X8dIpt21qPO1wrJRfKGi90nmhIwLF+XXCkPygoiIiICDer6Tz1M8h0pLn2N3ae5sj5y/z58+PGCOokOte9q3jm1cikVV4/UMrazHJ+ND6C8X30muXiDeTl5ZGZmcmgQYOMlnLF8PDsYUQGW/je1AFGSzFpB680Jm72a9jlWCwt+4h3nq3k7SNqhXuQxbMPsDX9OuFIf2ZmJhcuXPB4Y6Kz1+zm2v39fHhguj6TN3Wue1fxym4uDXoi2uTqq0uafD9fauUvO1Ta7aNCGRVj7Ar39miuXzcc6R8zZgyLFi1ys5rOM3u20Qqcpy3tZVVWfvz613x26IL7BHUSneveVbzSmBi4DrNLsFobnzyqayXPfFVMeY1kfO8A5g11b2wSZ7DXryOO9AcGBhIaGupmNZ3HqvH8h7a0v5txhnczzvLgqgxOFZS7T1Qn0LnuXcUrjUm9yxNdqXctAvCfjEsNLuXvG+f+2CTOYK9fRxzpv3DhAkePHnWzms5T73pDR9rSfvv4RK4fEculSis/fG0PlTW17hPWQXSue1fxSmNSp7kX68pK9bdszK7g06wKLD7w0ORIQvz1+Lvq9euKI/0nTpzgq3pHUx5MhcZrRtvSLoTgmcUp9O0RxP4zJfx2zWH3CesgOte9q+h91nsxp0pq+Oce1Xf/3THh9I/UPLC9F5CWlsaSJUuMlnFFExFk4e+3j8Xf14dXtuXw/t6zRksyseGVxiRc72UOpIwt4Y/bSqiuhWn9ApmeFGS0pE4xfrze/YyO9Pv7+xOsga+e6dONVuA8HdE+KiGCx29SYY8efmsfJy6WdrOqjqNz3buKVxoT3QfBXj9eRO4lKwlhviwdE67FOIk9ly7p7VPCkf5z585x+LDnda00p0jj2GQd1X7HhERuTulNeXUtP3zVc8ZPdK57V/FKY6IzH+w9S0ZJKf6+8NNJkQT6mX+Rp3Dy5Em21wevMTEUIQRPLRhF/+gQjpy/zJMfHjJa0hWPV16pyj1z1mCHSB/ai0TC+d6YcBIj9BwnOXLE87uC2sKR/nHjxnHrrbe6WU3nqQ+ypSOd0R4a4Mdfb78Kfz8fXtt+yiPGT3Sue1fxSmOiM2GBFibTl+uS9L4geyMWi4XAQNONjScxsncE/ztXjZ888tY+TuaXGazoysUrjYlFzxv6Bnr10nvQJzq6xmgJLuFI/9mzZzlQH3/Vg4mPN1qB8zij/c4Jidw4Kp46CSfyjB2M17nuXcUrfXMFeLa3kXZJSKgyWoJLeKv+7OxsCgoKSK4P8u2hDNDYJ6Iz2uvHT/JLqxjYy1gPBTrXvat4pTHR/cnEW+/sdcGR/gkTJnDVVVe5WU3n6d3baAXO46z2iCALEUGNJ36VtZYAP/fPKtS57l3FK7u5dJ+e99lnescZ91b9vr6+WDS4U3nzTaMVOI+r2qWUrNxximuf3sj5ksquEdUJdK57V/FKY2Ji0h3k5uayb98+o2WYtIGUsHb/Oc6WVPKBB8zuupLwym4uE5Pu4NSpUxQVFTF69GijpZg4wMdH8MclKWzLKuTmlCu4z8kAhGzDX7sQYkxbP5ZSeuSs6tTUNJmRsctoGU7z+ecZREZ6xopeZygu9vVK/XV1dYwZMwZfX89e4V9QAD17Gq3COXTWDvrrF0LsllKmOfPb9p5M/tjGNglc50yh9gghZgF/BnyBf0splzvItxBYDYyTUrZpKaqrXVVlLOfOBRAZqe/KS2/V7+Pj4/GGBCA7W98LWldrP3zuEs98fJQ/33YVoQHd3xGjc927Spu1K6W8tjsLF0L4An8DrgdygZ1CiPellIea5QsDfgR0yJdFjd6TiSgs1Lv30Vv1nz59Gl9fX1JTU90rqJPk5RmtwHm6UruUkl+8s5+vTxXzy/cO8sclKV23cwfoXPeu0qEBeCFEsBDiMSHEv2zfBwsh5nZB+eOBTClllpSyGngduKWVfL8Gfg90aHqG/k8megeS9lb9p0+fJiMjw71inCAnx2gFztOV2oUQPL1oNIEWH97ak+uWAXmd695VOnoL+V9gNzDZ9v0M8CbwoYvl9wFO233PBSbYZ7CN2/SVUq4RQvzM0Y6EEEuBpQDh4YmsWKHS4+Jg0CC1MtV+2t6iReqRND9fvQMkJ4O/v/rN2rUqzccH5s2DsjLYurUxiuO0aeqzxQL1vv969YIRIyAmpmlZCxfCyZNQUgInTqi04cMhKAj69IEPPmjMu3gxFBX5sW5dFKWlqkslNbWUykofAgIke/eqsL0REbUMGVJORIS1yVTW9PRizp/3p6LCl5wctXqzX78qgoJqiY+vZsOGyIa8M2YUUVLix7FjwZSUqLJGjy6juloQFFTH11+rBWChobUkJ5cRGlrbpKypU0u4eNFCdbUPWVnKzUhCQhVnz/pTXOzbJO+MGUUUFlrIzg5suPNPTi7DahWEhtY2RDcMDq4jNbWUwMA6Nm6MbAh0NmVKCfn5FqxWQWamcskfH19Njx5W4uOrWpSVn28hNzeA/Hw1lXfYMNVtFR5ey44dqqzAwDrS0i7j5yf58ssIamqUd+biYj8OHAimrk5w7JgqKza2hpiY6cycOaKhbdX/X6dPQ26uegGkpICvL0RHwyefqDR/fxUf3GpV0fjqgyhNn944lb3er1N8vFr81rt303a0eLFqq3l5jRetUaNUG7Rvs5s3w4IFykfdli1QWlrfNuDSJfDzgx07VFpMDAwbBrGxLc+PrCwoLlbvoNp2YKDS9aHdmb94sWrb27ap/au2oc6ZgACojyfWowekpqpuIPuy5s9Xx1NaCl98odKGDIHQUEhMhHffbVpWQQFkZEBhoUqbPBkqKyE4WB0vQEQEjBsHUVFhTAsbwceFB3jo9f309o+k9nIwFRVQ7wB64ECVv39/eOutpmXl5cGhQ3DxokqbMEH1fISFwaZNKi0sTGkICVF1X8+cOXD+vLq5rXeckJSk2kVSEqxe3bSsc+cgM1P9BiAtTQX6i4xsjOAYHKz+R39/WLOmsRdm5kyl0WqF+gmHffuq/yoxsWU7ys2FU6fgzBmVlpqqrnWu0OYAfEMmIXZJKdOEEF9LKa+ype2VUrr03CiEWATMklJ+1/b9m8AEKeV9tu8+wHrgHillthBiI/BQe2Mmw4alySNH9B2Af+GFI6Sm6utjKCMjxGv1jx071s1qOs+XX8LVVxutwjm6Q7uUkqWv7ObTQxcYn9SDlUsn4uvTPWEddK57cG0AvqO2qFoIEYQadEcIMRDoCp8ZZ4C+dt8TbGn1hAHJwEYhRDYwEXhfCNHmwWoW/qMFfn7tG3hPxlv15+TksHv3bjer6TwarKt0SHdoF0Lw+4Wj6RUWwI7sQv75xYmuL8SGznXvKh01Jr8E1gF9hRCvAp8DP++C8ncCg4UQ/YUQ/sCtwPv1G6WUJVLKaCllkpQyCdgG3Nzek4nuf6i3uiPRBUf6z507x8GDB92spvPExRmtwHm6S3uPEH+eWaw6Up795Bj7c0u6pRyd695VOmRMpJSfAguAe4CVQJqUcqOrhUsprcB9wMfAYWCVlPKgEOJJIcTNzu63pHvaidvYsiXCaAku4a36J06cyF133eVmNZ2nfuxER7pT+7QhvbhnchLWOsmP3viaiuquXwulc927SmfmcE4DpqC6uizAO10hQEq5FljbLO1xB3nTu6JMExOTK5OHZw/jy8x8jueV8tTaw/x6nmd7gNaJjk4N/jtwL7AfOAB8Xwjxt+4UdiXj6qwKo/FW/dnZ2ezcudO9YpxA5/rvbu2BFl/+362pWHwFr2zLYcPRrl0YonPdu0pHD/06YKaU8r9Syv8Cc+iC1e/dRZTeTmtJTy82WoJLeKv+CxcucOzYMfeKcYJ584xW4Dzu0D6ydwQPXj8UgOe/yOrSfetc967S0W6uTCARqF+S09eW5pHUr03QlcpKvW9vvFX/hAkTtJgaXK6vJxu3aV96zQD8/Xy4Y0Jil+5X57p3lTbPeiHEB0KI91FTdA8LITYKITagBsvD3CHQGeoXaelKRoax0eJcxdRvLPUL93TEXdp9fQTfmdKfQEvX+lrTue5dpb0nk2fcoqKLqdXXYS0A5eV639l7q/6srCxqamqYOHGimxV1Dp1vpozQfrmyht+vO8K90waSEBXs0r50rntXac/R4yZ3CTEx8XQKCgqwWq0eb0xMOsfyj47w6vZT5BZV8OK3xhstR1s6NGYihJgIPAcMB/xR7uLLpJTh3ajNacI8tgOuY6SlXTZagkt4q/5x48ZpMWaSnm60AucxQvtPrh/C2eIKHr1xuMv70rnuXaWjA/B/Ra1OfxNIA+4ChnSXKFfRvZur3sGjrpj6jaXe2aKOGKE9OjSA/3bRE4nOde8qHe7cllJmAr5Sylrb9OBZ3SfLNUzfXMbirfpPnDjB1q1b3aym8/hpHE7GaO1SSj4+eJ6aWuemhBqt30g6akzKbb6zMoQQfxBC/KQTv3U7Zfo6rAXgwIEQoyW4hLfqLyoqIrfez7wHU+9eXkeM1v7E+wf5/iu7+fsG55xBGq3fSDpqR7+JGie5D/gJap3Jwu4SdaXTr18/xo7tZ7QMp9m5E6/Ur8N4iYlrzEyO46Wvcnhu/XGuGxbDqAS9/cy5k446esyRUlZIKS9JKX8lpXzQ1u3lkejuNTgmxmgFrmHqNxad9RutffLAaL51tXIG+eCqDCprOjcAa7R+I2lv0eJ+IcQ+Ry93iewsgYFGK3CNYcOMVuAa3qp/y5YtbNFgVZrO9e8J2n8+cxgDokM4nlfKnz7tnPscT9BvFO11c3VFnHe3o/sgWGys0Qpcw1v1n6+Pp+rh6Fz/nqA9yN+XPy5JYeE/tvKvzVncMDKWsf16dOi3nqDfKNp8MrF1bzl81ecTQnzV/VI7Tn1MbV2xj9esI96qf9GiRSxatMi9YpxA5/r3FO1XJUbx/WkDkRJ+umov5dXWDv3OU/QbQVfNyNK8Y8nExMSkKT+eMZihsWFkF5Tzh3VHjZbj8XSVMdF7YYGJSQfYtGkTmzaZHoauFAL8VHeXn4/gxa3ZbD2Rb7Qkj8Zj14q4gu7xTDToSWkTb9VfUFBAQUGBe8U4gc7172nak/tEcN91gwD4+ep9lFa13d3lafrdSUcjLd4vhGjrEu1Ra86rqoxW4BpZXRuvx+14q/4FCxawYMEC94pxAp3r3xO1//DaQYyIDye3qILfrT3cZl5P1O8uOvpkEgvsFEKsEkLMEqKFw5JvdrEul9DdN1dxsdEKXMPUbyw66/dE7RZfH579RgrRoQGkJbXd7eGJ+t1FRxctPgYMBl4A7gGOCyGeEkIMtG0/4KwAm3E6KoTIFEI83Mr2B4UQh2xrWz4XQrS7tNp8MjEWb9W/YcMGNmzY4F4xTqBz/Xuq9mFx4WxZdi3zr0poM5+n6ncHnXH0KIHztpcViAJWCyH+4GzhQghf4G/AbGAEcJsQYkSzbF8DaVLK0cBqwOnyTExc4dKlS1y6kt3CXuHYR2XMu1xpoBLPpKNjJj8SQuxGXci/BEZJKX8AjMU1H13jgUwpZZaUshp4HbjFPoOUcoOUsj6y8jag7VsDICjIBUUewIjm5lQzvFX/Lbfcwi233NL6Rg9C5/rXQfu/N2cx5fcb+OLYxRbbdNDfXXR0rXgPYIH9QkUAKWWdEMKVVfJ9gNN233OBCW3k/w7wUWsbhBBLgaUAPXsmsmKFSo+Lg0GDID6+6YKiRYsgOxvy89U7QHIy+Pur36xdq9J8fGDePOWJeOtWuGyLmzRtmvpsscD27SqtVy/VmGJimpa1cCGcPAklJXDC5ox0+HBl9Pr0gQ8+aMy7eDFcvAgrV6r8AFOmQHm5chNT7wG9Rw9ITYWePZuWNW8enDqlwoces3mCGDIEQkOhXz94552mZRUUQEYGFBaqtEmTVDdhSAhs3qzSwsNh4kSIiGha1ty5cPYsVFbCoUMqbcAAOHNG1cPq1U3LunABjhyBvDyVNn48WK1q/xs3qrTQUHW8wcHw7rtQZ/MEPmcOnD8PNTWwf79K69dP1XVSUlNdixcrXVlZcO6cShszRr1HRcHnn6vPQUFw3XXKY8JHH0F1tUqPjVXeX2trYe9elZaQoF59+7Ys6/RpyM1VL4CUFPD1heho+OQTlebvD7Nnq+Ndvx4qKlT69OmNi2z37FHv8fGqHnv3bllWdraqvxzbmThqlGqD9m02J0e59SgvVzHJ60PJpqereBt+fo3ebWNiVN7Y2JbnR1aWGgOo77oZMUK1wd694cMPm+oqKYFt2xrjeUydqs6ZgAD4yrak2VGbnT9faS4tVfV16FBjm01MVO3AvqzmbXbyZNUGg4MbY7BHRMC4cer/ti/rpptU+6yogMO2sfSBA1X+/v3hrbealpWXp/RctNmNCRPgRHYd1dY6VrxVyKGoXoSFKQ0hIaod1Z8L9W22uhoO2AYCkpJUu0hKanl+nDsHmZnqNwBpaar9R0aqNgPqGNPTVXtas0adDwAzZyqNVivsszm66ttX/VeJiS3bUW6uuk6cOaPSUlPVtc4VhOq9MgYhxCJglpTyu7bv3wQmSCnvayXvnSivxdOklG2OiowenSb37dvVHZLdQm6uunDpirfq/+yzzwCYMWOGmxV1Dp3rXwft1to6duUUMXFAzxbbdNDfFkKI3VLKNGd+a/Q6kzMod/b1JNjSmiCEmAE8CtzcniGBxjt6XbG/69MRb9VfUVFBRf0jhQejc/3roN3P16dVQwJ66O8ujDYmO4HBQoj+tuBbtwLv22cQQlwF/BNlSPIM0GhiAsBNN93ETTfdZLQMEw9id04R33xhe7uLGa8EDDUmUkorquvqY+AwsEpKeVAI8aQQ4mZbtqeBUOBNIUSGEOJ9B7szMTExcRtSSp788BCbj+e3u5jxSsDQMZPuIjU1TWZk6DtmUlCgBil1xVv1f2IbTb/hhhvcrKhz6Fz/umk/ev4yc5/bTE2t5NXvTmBYVLRW+puj85hJt6D7Cnjdx3y8VX9NTQ019dNnPBid61837UPjwnjgusEALHtrH+fzr9zuLq80JmVlRitwjW3bjFbgGt6q/8Ybb+TGG290rxgn0Ln+ddR+b/pARvZWvrt+/f4Ro+UYhlcaE92fTHRfZG3qNxad9euo3eLrw9OLlKv6bQU5bMvyfM/S3YFXGhMTk+5g3bp1rFu3zmgZJh7IiN7h/PBa5ap+2Vv7OhyZ0ZvwSmMSGmq0AteYOtVoBa5h6jcWnfXrrP2H1w6if1QYOQXlPP3xlReZ0SuNSb0LDl3RfczHW/XPmjWLWbNmuVeME+hc/zpr9/fz4fupKfjaIjPuyi40WpJb8Upj4qqPGaMJCDBagWuY+o1FZ/06awcYHhfB968ZgJQqMmNljeYDuJ1A88tu69Q7ttOVesd4uuKt+tesWcOaNWvcK8YJdK5/nbWD0v/A9MEMigklK7+Ml7/KNlqS2+io12ATkysei8VitAQTDQi0+PL0otFsOHqReyb3N1qO2/BKY+Kn+VH16GG0AtfwVv2evvK9Hp3rX2ft0Kj/qsQorkpsO8Svt+GV3Vy6B8dKTTVagWuY+o1FZ/06a4fW9ReVVbPuwDm3a3E3mt/Dt47uTyY6+/YB79X/gS2Kmad7Dta5/nXWDi31l1TUcP2fvqC4vJr37wthRO9wY4S5Aa98MqmPXKcr9lHRdMRb9QcFBRGkwWOvzvWvs3ZoqT8iyMKcUXGM7RdFaIDmd7nt4N1HZ2LShXh6hEUTz+TRG4dj8fHBx0cYLaVb8conExMTExNPIcDPt8GQSCkpKfd8z9PO4JXxTFJS0uTevfrGM7lwAWJjjVbhPN6q/7333gPglltucbOizqFz/eusHdrWf+FSJT9dtZfyaitv3jsZXw98UjHjmTSjutpoBa6Rk2O0AtfwVv3h4eGEh3v+AKrO9a+zdmhbf6DFl2MXLrPnVDEvbc12myZ34ZXGRHffXLqv4PdW/ddeey3XXnute8U4gc71r7N2aFt/RJCF384fBcDTHx/lVEG5m1S5B680JpWVRitwjWPHjFbgGqZ+Y9FZv87aoX3914+I5eaU3lTU1PLw2/vwpmEGrzQmJibdwdtvv83bb79ttAwTzfnlTSPoEeLP1hMFvL7ztNFyugzDjYkQYpYQ4qgQIlMI8XAr2wOEEG/Ytm8XQiS1t8/AwG6R6jaGDDFagWt4q/6ePXvSU4NVdTrXv87aoWP6e4YG8KubRwLw2zWHOVdS0c2q3IOhxkQI4Qv8DZgNjABuE0KMaJbtO0CRlHIQ8Cfg9+3tV3cX9LoH9/JW/dOmTWPatGnuFeMEOte/ztqh4/rnjo7n+hGxlFZZueXXBxg3XnL//XBa4wcVoy+744FMKWWWlLIaeB1oPu/yFuAl2+fVwHQhRJtz6vz9u1ynW0lMNFqBa5j6jUVn/Tprh47rF0LwP+OTkVV+5PnlcbjsDP/8J6Sk6GtQjF4B3wewr7pcYIKjPFJKqxCiBOgJ5DvaqeXybnjNgb0Z/08YtFR9zvwX7Pi+Y3W32w2OfTQWiva0nm/g92DCv9Tnwt2wro1p2rN2QY+x6vP2pXDi+RZZ4gCixsDs3Y2Jjo4HPO6Y4lo5JkCbY4qDDv1PgEceU5yjfWpwTHHQ5ecT4LZjiuvE/3QVkDPOtn10Y9Y//G0XP19u4DE5idHGpMsQQiwFlgKMbSOEwKZNcPgzWLQISrMhqY19rlihuszmzYOIanAUBO7QYfjia+jVC8YkQVsRDFavhvw6GD4chl+GGAf5Cotg1Qr1ecoUSG5jn/XHBHDbOIho55jq+W6C4wZgX36/cNUP6Yg9e2BHpvo8txckOMhXUQkfvQ15eer7vW0s2bh0CV7/l5rmPdwC09pwiVVQ0OgTaWEI9PJtPV/eRSg5Dp9/DtE+sKiNLokDB+CyBfbuhWsCYYSDp11rLRzIgNxc9WrrmIpL4PJpWL8ekqxtH9P+/dC7tzquto7p/AU4tQPi4mDHuraP6WQ2XMxUjlADDzs+pov5IPIhKwuKi6Etx/ubNkFyFJSUwMUdLe8E7Vm1SnnV7dkT6vIdH9Ohw3C+THUZDYiE6Db2uXo1DJmoZnAOKgJHHuwv5sNbK+Cmm+DMGdUl0tYxHf4MFi+G6nMQ30beFSsgLAwmT4YEKziKeFN/jUhKgsRQ1afviM2bIXwFpKVB4kXH14j8AlhtO0dnzmz7umN/jbhzInRLb6KU0rAXMAn42O77I8AjzfJ8DEyyffZDPZGItvabmDhW6sw//mG0Atcw9RuLzvp11i5l5/Tfd5+UFouUvuFlsu+PP5IJ930iAyIr5H33dZ++9gB2SSev54a6UxFC+AHHgOnAGWAncLuU8qBdnh8Co6SU9wohbgUWSCmXtLXf1NQ0mZGhrzuVggK9XXGb+o1FZ/06a4fO6T99Wo2RlJaCb5+LyIIIgv382bsX+vbtXp2O0NadipTSCtyHevo4DKySUh4UQjwphLjZlu0FoKcQIhN4EGgxfbg5Vmt3KXYPBQVGK3ANb9W/atUqVq1a5V4xTqBz/eusHTqnv29f1Y36/e/D6JhefO9uYw2Jqxg+ZiKlXAusbZb2uN3nSmBxZ/ZZofm07YwMvefbe6v+hARHo0Gehc71r7N26Lz+vn3huecav1db6/jTp5lclRhJ+lBHoyWeieHGpDvQ/cmksNBoBa7hrfonT57sXiFOonP966wdXNf/1p5c/vz5cfpEBrHhoXT8/YxevdFxvNKYmJiYmOjI4rEJbD1RwJ0TErUyJOClxkT3VbSa3AA7xFv1r1y5EoDbbrvNjWo6j871r7N2cF2/n68Pz912VdeIcTN6mb4OorsLet29Hnur/v79+9O/f1uz+T0DnetfZ+3gun5fX19SU1NJSUlhzJgx/OvNjyivtlJRUcG0adOora3t9D7XrVvH0KFDGTRoEMuXL29Ir66u5pprrsHaReMCXvlkortvruBgoxW4hrfqnzhxonuFOInO9a+zdnBdf1BQEBkZGQDc/4f/8sBPf86FoDfokbOBBQsW4OvrYKWnA2pra/nhD3/Ip59+SkJCAuPGjePmm29mxIgR+Pv7M336dN544w3uuOMO14TjpU8mugfY2bLFaAWuYeo3Fp3166wdulZ/UrgPvoGh/OfLk/zrPy81hIs+ceIEvXr1IikpidTUVHr06MHAgQO5dOlSi33s2LGDQYMGMWDAAPz9/bn11lsbwk8DzJs3j1dffbVL9HqlMTEx6Q5effXVLjvxTExao6KigtTUVIYNG8aTyx7g2/c9RJ21hiPHM4nroxagDBw4kClTpvDKK6+QkZHB6NGjeffdd1sNKX3mzBn62i1cSUhI4MyZMw3fk5OT2blzZ5do90pj0sknQY8joi3nWhrgrfqHDBnCEA0WQehc/zprB9f113dzHTlyhHXr1vH5isdJCKqhzhLCc+uPN+Q7ePAgycnKY9/hw4cZOnSoU+X5+vri7+/P5cuXXROOlxqTkBCjFbjGuHHt5/FkvFX/uHHjGKfBwWkg0SE6a4eu1T9p0iQKCvL55c2jkNZqVmzK4sCZEioqKqisrCQqKorTp08THR2Nv4O4G3369OG0nU/73Nxc+vTp0yRPVVUVgV0QUdArjYnuTyZRUUYrcA1Tv7HorF9n7dC1+o8cOUJtbS3TrxpMiL8P1uoqHnpzL3v3HWD48OGAeiqp/wwwffr0Jt1Y48aN4/jx45w8eZLq6mpef/11br755obtBQUFREdHY7E48nfccbzSmBQVGa3ANerdqeuKt+p/+eWXefnll90rxgl0rn+dtYPr+uvHTFJTU/nGN77BSy+9hK+vL/PmziK85ARHzl/mubc3NHRxBQUFsWfPHo4cOUJdXR2ZmZn06NHoiN/Pz4+//vWvzJw5k+HDh7NkyRJGjhzZsH3Dhg3ceOONromuL6tL9mJicgVgfxKamHQHjtaR/Oj++/nFk8s50nM4O/yS+eAn9wIwdepUsrKyADhw4AALFy4kKKhpoJw5c+YwZ86cVvf72muvNVl74gpe+WRiYtIdjB07lrFjxxotw+QKZMyYMSy5eRa3j+tDTa3kZ2/uw1rbdHV2cnIyzz77bIf3WV1dzbx587psUomh8Uy6i5SUNLl3r77xTM6cgWZjZFph6jcWnfXrrB26X39plZWZf/qCM8UV/GzmUH547aAu3b+28Uy6i+pqoxW4ht34mZZ4q/4XX3yRF1980a1anEHn+tdZO3S//tAAP363YBT+fj4EeJgjSK8cM9HdN5fu8Vi8VX9qaqpbdTiLzvWvs3Zwj/5rhvRiy7JriQlzfTpvV+JZpq2L0N1Z3OHDRitwDW/VXz/LxtPRuf511g7u029vSKqtnnH37JXGxMSkO6itrXXKa6uJSXfxzte5TP3Dek5cNN4hoVcak4AAoxW4xsCBRitwDW/V/8orr/DKK6+4V4wT6Fz/OmsH9+vfcryAC5eqeHNXrnsLbgWvHDPRfQX8le6fyGgc6R8zZox7hTiJzvWvs3Zwv/7H545gyuCezEs1fgqcVxoT3Z9MNIi/1Cbeqn/06NHuFeIkOte/ztrB/fojgi3MvyrBvYU6wLBuLiFEDyHEp0KI47b3Fl5thBCpQoivhBAHhRD7hBDf6Mi+dXen8tZbRitwDW/VX1NTQ01NjXvFOIHO9a+zdjBWf9bFUp54/yC1dcasHTRyzORh4HMp5WDgc9v35pQDd0kpRwKzgP8nhIh0n0QTk0bMeCYmnkptneSe/+7kxa3ZvLg12xANRhqTW4CXbJ9fAuY1zyClPCalPG77fBbIA3q5S6CJiT1paWmkpTm1ONjEpFvx9RE8PncEAE9/fIST+WVu12CYOxUhRLGUMtL2WQBF9d8d5B+PMjojpZQtJlYLIZYCSwFiYhLH/upXOQDExcGgQRAf39Sj56JFkJ0N+fnqHSA5Gfz91W/WrlVpPj4wbx6UlcHWrVAfQ2baNPXZYoHt21Var14wYgTExDQta+FCOHkSSkrgxAmVNnw4BAUp1wsffNCYd/FiyMqCzEyVH2DKFCgvh8BApQGgRw9ITYWePZuWNW8enDqlQhcfO6bShgyB0FDo1w/eeadpWQUFkJEBhYUqbdIkqKpSMWE2b1Zp4eEwcaIaXLQva+5cOHtWres5dEilDRgAQsBVV8Hq1U3LunABjhyBvDyVNn48WK1q/xs3qrTQUHW8wcHw7ruNC1DnzIHz56GmBvbvV2n9+qm6TkpqqmvxYqUrKwvOnVNp9WPnUVHw+efqc1AQXHcd+PnBRx81ek4YNw5qa9Vr716VlpCgXn37tizr9GnIzVUvgJQUNQkkOho++USl+fvD7NnqeNevb1zcNn16Y7fsnj3qPT5e1WPv3i3Lys5W9ZejmjejRqk2aN9my8vhzjvV+5YtjWGs09Ph0iV1vDt2qLSYGBg2DGJjW54fWVlQXKzeQbXtwECl68MPm+oqKYFt29T+AaZOVedMQAB89ZVKc9Rm589Xx1NaquogNLSxzSYmqnZgX1bzNjt5smqDwcGNYXMjItT/GBXVtKybblKr1CsqGteEDByo8vfv37SbavFiVdeHDsHFiyptwgTVBsPCYNMmlRYWpjSEhMD//V9jHPj6NltdDQcOqLSkJNUukpJanh/nzqnz/vx5lZaWptp/ZKRqM6D2nZ6u2tOaNUoLwMyZSuNfdmSwJfcMCQFRLBs3iYQ+gsTElu0oN1ddJ+pX7KemqmvdhAnOu1PpVmMihPgMiGtl06PAS/bGQwhRJKVsNRqAECIe2AjcLaXc1l65yclp8sABfX1zHT6sjI2ueKv+Sttq2K4IJNSd6Fz/OmsH4/UXl1dz/Z++4OLlKh67cTjfnTqgU7/3WN9cUsoZUsrkVl7vARdsRqLeWOS1tg8hRDiwBni0I4YE9HfJUH+Xryveqv/111/n9ddfd68YJ9C5/nXWDsbrjwz253fzRwHw9MdHyXLjYkYjx0zeB+62fb4beK95BiGEP/AO8LKUcnXz7Y6wWrtEn2HUP1LrirfqnzBhAhMmTHCvGCfQuf511g6eoX/GiFgWjOlDlbWOh97c67bZXUYak+XA9UKI48AM23eEEGlCiH/b8iwBrgHuEUJk2F6phqg1ueIZPnx4kxCpJiaeyi/njiQ2PIA9p4p5YUuWW8o0zJhIKQuklNOllINt3WGFtvRdUsrv2j7/n5TSIqVMtXtltLfvkJBuFt/NaHDz2ybeqr+8vJzy8nL3inECnetfZ+3gOfojgi38boHq7nrmk2Nk5l3u9jK90jeX7vG+NFgX1ybeqn/VqlWsWrXKvWKcQOf611k7eJb+64bFsnhsAtXWOn66am+LyIxdjVcaE919c4WFGa3ANbxV/6RJk5g0aZJ7xTiBzvWvs3bwPP3/e9MIekcEsje3hJe+yunWsrzSmFzu/ie6bqV+/rqueKv+oUOHMnToUPeKcQKd619n7eB5+sMDLfx+0WiWpCWwOK17fXh5paPH1qipqSE3N7dhrYAnM2aMXkGCAgMDSUhIwGKxGC2lWym1rf4LDQ01WImJSceZOrgXUwd3v+MQrzQmrXVz5ebmEhYWRlJSEmrBvedSUKBWCeuAlJKCggJyc3Ppb3OZ6mmP+p3Fkf7VtiXL99xzj/vEOIHO9a+zdvB8/ZU1tXyVVcC1Q2O6fN9eaUxam81VWVmphSEB5UZCF4QQ9OzZk4t2E+wnTzZQUBfgSP+UKVPcK8RJdK5/nbWDZ+uvrKll7nNbOJlfxts/mExK38gu3b9XGhNHA/A6GBJQPnJ0onm96j4125H+QYMGuVeIk+hc/zprB8/WH2jxJX1ILwTg59v110LNLlsdQ/d4JsXFRitwDXvHfDriSH9JSQkl9d43PRid619n7eD5+h+aOZQP7p/CyN5dHxLSK42JbqSnp7NrV6NjytbWyTz11FMOf//mm28yfPhwrr32Wnbt2sUDDzzQHTI7TF33Tmfvdhzpf+edd3jH3u2yh6Jz/eusHTxff6DFl0BLY9dNcXl1l+3bK7u5vJGnnnqKX/ziF61ue+GFF3j++ecb+vS7KuaG1WrFz89sIvVcc801RkswMekSyqutPPbuAbZnFbLux1MJC3R9JqZXXikiOvAEl/Twmk7tM7lPOB/eP7XF77OX39ih32dnZzNr1izGjh3Lnj17GDlyJC+//DLB9cEPbKxcuZLf/vYpQHLjjTfy+9//nocffpiKigpSU1MZOXJkk2h/Tz75JFu2bOE73/kON998MzfeeCPPPPMMH374IRcvXuT222/n7NmzTJo0iU8//ZTdu3dTWlrK3LlzOWALsvDMM89QWlrKE088QXp6OqmpqWzZsoXbbruN9PR0HnzwQUpLS4mOjubFF18kPj6+zWOdM6dDVeKxONI/YEDn3Hkbhc71r7N20Ee/xdeHzLxSzhRX8OQHh3h6cYrL+/TKbi5Pcmlgz9GjR/mf//kfDh8+THh4OH//+9+bbD979izLli3jww/Xk5GRwc6dO3n33XdZvnw5QUFBZGRktAgb+/jjj5OWlsarr77K008/3WTbr371K6677joOHjzIokWLOHXqVId0VldXN3SX3X///axevZrdu3fz7W9/m0cffbTd39cH99EVR/qLiooo0mBATuf611k76KPf4uvDs0tS8Pfz4c3duXx80HXhXvlk0hHfXB19oujK3/ft25err74agDvvvJO//OUvPPTQQw3bd+7cSXp6Oj179sLPD+644w6++OIL5s2b55TGLVu2NPTxz5o1i6ioVmOPteAb3/gGoIzfgQMHuP766wGora1t96kEGiMW6ooj/e+9p6IkePo6E53rX2ftoJf+QTFhLJs1jF9/eIhH3t7PmMSOXR8c4ZVPJp4aHKv5FFpHU5W7W7+fnx91diOFzb0ChNjmN0opGTlyJBkZGWRkZLB//34+qY9D2wb1IUp1xZH+9PR00tPT3arFGXSuf521g376vzU5ickDe1JYVs0jb+9zaV9eaUw8lVOnTvGVLSD2a6+91mIR3Pjx49m0aRMFBfnU1taycuVKpk2bBoDFYqGmk/13V199dYOX208++aShiyY2Npa8vDwKCgqoqqriQ/uA3nYMHTqUixcvNmiuqanh4MGDndLgTSQlJZGUlGS0DBOTLsPHR/DM4hTCAv347HCrwW47vq8u0uRRBAQYraB1hg4dyt/+9jeGDx9OUVERP/jBD5psj4+PZ/ny5SxadC0pKSmMHTuWW265BYClS5cyevRo7rjjjg6X98tf/pJPPvmE5ORk3nzzTeLi4ggLC8NisfD4448zfvx4rr/+eoYNG9bq7/39/Vm9ejXLli0jJSWF1NRUtm7d2m65ul9vHenPz88nPz/frVqcQef611k76Km/d2QQv5mX7PqOpJRe9xo+fKxszqFDh1qkuZOTJ0/KkSNHdihvaWnXlFlZWSlramqklFJu3bpVpqSkdM2OW8G+fnfu7LZi3IIj/f/973/lf//7X7dqcQad619n7VLqq7+urk5+mXlRArukk9ddrxyA9/c3WoFrdJX+U6dOsWTJEurq6vD39+f555/vmh23g453Z/Y40j99+nS36nAWnetfZ+2gr34hBJMHRru0D6/s5vLE2ZtJSUkN6zrao6v0Dx48mK+//pq9e/eyc+dOxo0b1zU7bgebc11tcaS/b9++9O3b171inEDn+tdZO+iv3xW80pg4Quoez9dDuVLqNS8vj7w81wYpTUy8FcOMiRCihxDiUyHEcdu7w0nOQohwIUSuEOKvzpYXGBhIQUHBFXPhcxfSFs8kMDDQaCndztq1a1m7dq3RMkxMPBJh1MVVCPEHoFBKuVwI8TAQJaVc5iDvn4Fetvz3tbfv1NQ0mZGxq0maTpEWa2v1imPfPNKiTsG9WsOR/jNnzgDQp08fNyvqHDrXv87aQX/9QojdUkqnnPsZOQB/C5Bu+/wSsBFoYUyEEGOBWGAd0KGDbG05hsViaYgE6OkcOADDhxutwnnOndP7hHKk39ONSD0617/O2kF//a5gpDGJlVKes30+jzIYTRBC+AB/BO4EZrS1MyHEUmApQGRkIitWqPS4OBg0COLj4c03G/MvWgTZ2ZCfr94BkpPVTKq4OKjvzfDxgXnzoKwMtm6Fy5dV+rRp6rPFAtu3q7RevWDECIiJaVrWwoVw8iSUlMCJEypt+HAICoI+feCDDxrzLl4MmzfD/v0qP8CUKVBeDoGBSgNAjx6Qmqoarn1Z8+bBqVNQWgrHjqm0IUNU9MZ+/cDeg/rixepOKiMDCgtV2qRJUFWlgvxs3qzSwsNh4kTlQNO+rLlz4exZqKyEQ4dU2oABan9xcU0HIxcvhgsX4MgRqB92GD8erFa1/40bVVpoqDre4GAVG6J+of6cOcrvUU2NqhtQxxMTo2bQ2OtavFjpyspSJzfAmDHqPSoKPv9cfQ4KguuuAz8/+Oijpq4wysvVE+Levep7QgKEhZ0nNhY2boxrUtbp05Cbq14AKSnqyTI6GuodBvj7w+zZ6njXr2/0cjB9euOEiz171Ht8vKrH3r1bHld2tqq/nByVNmqUaoP2bXbfPnjiCXUMW7aotgCQng6XLqnj3bFDpcXEwLBhEBvb8vzIylKxdbKyVNqIEaoN9u4N9utcFy9WbXXbNrV/gKlT1TkTEAC2Na8O2+z8+ep4Skth1SqVp77NJiY2jRHSWpudPFm1weBgdbyg2uq4cer/ti/rppvgzBlV/4cPq7SBA1X+/v3hrbealpWXp9p2fSDRCRNUGwwLg02bVFpYmNIQEgJ//zuMHq3S69tsdXXjyvikJNUukpJanh/nzkFmZqN/r7Q01f4jI1WbAXWM6emqPa1Z03jjPHOm0mi1qv8foG9f9V8lJrZsR7m56jphe9gmNdX1oHzd2s0lhPgMiGtl06PAS1LKSLu8RVLKJuMmQoj7gGAp5R+EEPcAaR3p5urXL03m5OxqL5vHsmIF3Huv0Sqcx1v1v/jii4Dn++bSuf511g766/fYbi4ppcOnCSHEBSFEvJTynBAiHmhtmswkYKoQ4n+AUMBfCFEqpXy4mySbmDhk1qxZRkswMfFYjByAfxoosBuA7yGl/Hkb+e+hg08mQojLwNEuE+t+ogHP99vhGFO/seisX2ftoL/+oVLKMGd+aOSYyXJglRDiO0AOsARACJEG3Cul/K4L+z7q7KOaJyCE2GXqNw5Tv3HorB28Q7+zvzXMmEgpC4AW/imklLuAFoZESvki8GK3CzMxMTEx6TRX1Ap4ExMTE5PuwVuNyb+MFuAipn5jMfUbh87a4QrWb9gAvImJtyKEWAGsBJ5ArZ+SwL+klH82UpeJSXdiGhMTky5GCJEB3IhamLtHCBEG7AbmSSkPGSrOxKSb8Mp4JiYm3YkQYiCwDSgDioFEoAi4CugDHJNSngHOAEgpLwshDtu2mcbExCvResxECDFLCHFUCJFpW6vSfHuAEOIN2/btQogkA2Q6pAP67xFCXBRCZNherkyX7lKEEP8RQuQJIVoN0iIUf7Ed2z4hxBh3a2yLDuhPF0KU2NX94/XbpJQngC3AN6WUqcA+1FPHJWA2yo+c/b6SUIZmexdp7yuE2CCEOCSEOCiE+FEreTy2/juo32H9G40QIlAIsUMIsdem/1et5PHYa08H9Xf+2uNsiEajX4AvcAIYAPgDe4ERzfL8D7DC9vlW4A2jdXdS/z3AX43W6kD/NcAY4ICD7XOAjwABTAS2G625k/rTgQ/b+P0xlKdrgAuAv+3zx0Bvu3yhqC6uBV2oPR4YY/scZtPSvO14bP13UH+b9W+wfgGE2j5bUDcJE5vl8eRrT0f0d/rao/OTyXggU0qZJaWsBl5HeSK25xaUR2KA1cB0IYRwo8a26Ih+j0VK+QVQ2EaWW4CXpWIbEGlzm+MRdEC/Q4QQQUCglLJICNEXyJdSVgshgoFIKeVZWz4L8BbwqpTy7S7Ufk5Kucf2+TJQ34Vmj8fWfwf1eyy2OrW5z8RiezUffPbYa08H9XcanY1JH+C03fdcWjbIhjxSSitQAniKg+iO6AdYaOumWG27cOlCR4/Pk5lk6wr4SAgx0i59BOoCCDDc7vO1wAZQ3UzAC8BhKeWz3SWwjS40Leq/nS5AR/VvOEIIX9tEizzgUymlw/r3wGtPR/RDJ689OhuTK4EPgCQp5WjgUxrvdEy6nz1APyllCvAc8K7dtpFA/VhLBTBGCDGMpuMlVwPfBK6z63ee05UChRChqCefH0s1XqMV7ehvq/4NR0pZK9V4WQIwXgiRbLCkTtEB/Z2+9uhsTM4A9tYywZbWah4hhB8QARS4RV37tKtfSlkgpayyff03MNZN2rqCjvw/HouU8lJ9V4CUci1gEUJE276/LKX8qe3zZinlACnlEWAy8KUtfYuUUkgpR0spU22vLov524EuNI+u//b0t1X/noSUshj1NNrcpbQnX3sacKTfmWuPzsZkJzBYCNFfCOGPGuR6v1me94G7bZ8XAeulbXTJA2hXf7M+7ptp7E7RgfeBu2yziiYCJbIxGJrHI4SIq+/jFkKMR50rbV4MpJRjpJStxPnscm0d6ULz2PrviH5n6t9dCCF6CSEibZ+DgOuBI82yeey1pyP6nbn2aLvOREppFSp41seomVH/kVIeFEI8CeySUr6ParCvCCEyUYOttxqnuCkd1P+AEOJmwIrSf49hgpshhFiJmnETLYTIBX6JGshDSrkCWIuaUZQJlAPfMkZp63RA/yLgB0IIK6or61ZPuRjQ2IW239bvDfAL1HoXHeq/I/o9uf7jgZeEEL4oI7dKSvmhLtceOqa/09cecwW8iYmJiYnL6NzNZWJiYmLiIZjGxMTExMTEZUxjYmJiYmLiMqYxMTExMTFxGdOYmJiYmJi4jGlMTExMTExcxjQmJiYmJiYuYxoTExM3IIQYZ3OaFyiECLHFkdDKn5OJSVuYixZNTNyEEOI3QCAQBORKKX9nsCQTky7DNCYmJm7C5oNtJ1AJTJZS1hosycSkyzC7uUxM3EdPVOTFMNQTiomJ12A+mZiYuAkhxPuoiJr9gXgp5X0GSzIx6TK09RpsYqITQoi7gBop5Ws2b61bhRDXSSnXG63NxKQrMJ9MTExMTExcxhwzMTExMTFxGdOYmJiYmJi4jGlMTExMTExcxjQmJiYmJiYuYxoTExMTExOXMY2JiYmJiYnLmMbExMTExMRl/j969Pnk4uMlGQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0.5, 3.5, 100)\n",
    "y = np.sin(x)\n",
    "y1 = np.random.randn(100)\n",
    "\n",
    "plt.plot(x,y,\n",
    "         ls = '-.',\n",
    "         lw= 2,\n",
    "         label= \"plot figure\",\n",
    "         )\n",
    "plt.legend(loc=3)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y_label')\n",
    "plt.annotate('$y = \\sin(x)$',\n",
    "             xy = (3*np.pi/4, np.sqrt(2)/2),\n",
    "             xytext = (2.5,.9),\n",
    "             arrowprops = dict(\n",
    "                 arrowstyle=\"->\",\n",
    "                 connectionstyle = \"arc3\",\n",
    "                 color = 'b',\n",
    "                 lw = 3,\n",
    "                 alpha = .4\n",
    "             )\n",
    "             )\n",
    "plt.xlim(0,3.5)\n",
    "plt.grid(True, c = \"b\",alpha = .8 , lw = .51, linestyle = \"-.\")\n",
    "# 添加垂直的参考线。\n",
    "plt.axvline(np.pi/2, ymin= -.2, ymax = 1.0,color = 'gray',ls= ':')\n",
    "plt.text(np.pi/2,-.5,'$\\pi/2$')\n",
    "# 添加水平的参考线。\n",
    "plt.axhline(y=0, lw = 2, c = \"orange\", ls = \"--\")\n",
    "# 绘制垂直的参考区域\n",
    "plt.axvspan(xmin=.5, xmax = np.pi/2,ymin=np.sin(.5),alpha =.4,facecolor = 'gray')\n",
    "# 添加文本说明\n",
    "for dot_x ,text in zip([np.pi/2,np.pi],[\"A($\\\\frac{\\pi}{2},1$)\",\"B($\\pi,0$)\"]):\n",
    "    plt.scatter(dot_x,np.sin(dot_x),c = \"blue\",marker='o',s=30)\n",
    "    plt.text(dot_x,np.sin(dot_x)-.1 , text)\n",
    "plt.title(\"chapter_1 test figure title\")\n",
    "plt.savefig('chapter_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlim(0.0, 3.5)\n",
    "plt.scatter(x,y,\n",
    "            c ='blue',\n",
    "            lw = 2,\n",
    "            label = \"scatter\",\n",
    "            s = y,\n",
    "            )\n",
    "plt.legend(loc= 'upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
